Problem: Solve for $x$ and $y$ using elimination. ${-2x+y = 0}$ ${-5x-y = -14}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-7x = -14$ $\dfrac{-7x}{{-7}} = \dfrac{-14}{{-7}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-2x+y = 0}\thinspace$ to find $y$ ${-2}{(2)}{ + y = 0}$ $-4+y = 0$ $-4{+4} + y = 0{+4}$ ${y = 4}$ You can also plug ${x = 2}$ into $\thinspace {-5x-y = -14}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ - y = -14}$ ${y = 4}$